Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C32×SD16 ⋊ C2 |
| Sylow | C32 ⋊ AGL(1,ℤ/8) |
204 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,2,4,5)(3,8,7,6)(12,13,14);(2,6)(3,7)(5,8)(9,10,11);(2,5)(6,8)(10,11)(13,14)Polycyclic presentation:
2^5,3^2|c^2=e,d^2=e,c^a=ce,f^a=f^2,g^a=g^2,c^b=cd,d^b=de,d^c=de39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#914, #10594746, #10594751, … |
| maximal normal subgroup of | D3×#914, #10594746, #10594751, … |
| maximal quotient of | #10592463, #10592465, #10592469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 771);